An exact algorithm for cost minimization in series reliability systems with multiple component choices

In this paper, we present an exact method for cost minimization problems in series reliability systems with multiple component choices. The problem can be modelled as a nonlinear integer programming problem with a nonseparable constraint function. The method is of a combined Lagrangian relaxation and linearization method. A Lagrangian bound is obtained by solving the dual of a separable subproblem. An alternative lower bound is derived by 0-1 linearization method. A special cut-and-partition scheme is proposed to reduce the duality gap, thus ensuring the convergence of the method. Computational results are reported to show the efficiency of the method.